JLT said:
Occam's razor kind of best.
By that you mean the derivation that requires the fewest starting assumptions?
Most derivations start with two straightforwardly stated and universally applicable assumptions, namely Einstein’s postulates. From there it's just logic and a lot of high school math.
However it is
a lot of that high school math.
@malawi_glenn's post #2 in this thread follows the same path that Einstein and his contemporaries took to get to ##E=mc^2## from the postulates, but there's a fair amount of preliminary work required to get to where we can set up the integral. In #7
@Dale uses the norm of the four-vector, an approach that is much more aligned with modern thinking, but again there's a lot of preliminary work required to get to that four-vector formulation. I was tempted to post my "simplest" derivation: Set ##p=0## in the general relationship between mass, energy, and speed/momentum:$$E^2=(m_0c^2)^2+(pc)^2$$but of course that just invites the question, where did that relationship come from? And the answer is the same as for the other two: Start with Einstein's postulates and do a lot of high school math.
There's no way of getting to ##E=mc^2## without understanding all of special relativity, the same way that I can't fill the house with the delicious smell of a baking cake without actually baking a cake. That makes MalawiGlen's second answer, the one in #6, perhaps the most useful one.